Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation

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Modeling and analysis of functionally graded sandwich beams: a review (2019, background): “Fallah and Aghdam [171] presented analytical expressions for geometrically nonlinear vibration and postbuckling analysis of FG beams resting on nonlinear foundation.”
Nonlinear bending analysis of FGM beams based on physical neutral surface and high order shear deformation theory (2013, background): “Fallah and Aghdam [23,24] investigated nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation.”
Nonlinear analysis of shear deformable FGM beams resting on elastic foundations in thermal environments (2014, methodology): “As a second example, the nonlinear to linear frequency ratios ωNL=ωL for an isotropic beam with L/r1⁄41000 are calculated and listed in Table 3 with homotopy analysis method results of Fallah and Aghdam [37] and Pirbodaghi et al.”
Geometrically nonlinear free vibration analysis of axially functionally graded taper beams (2015, background): “Some research works are also available on the effect of nonlinear elastic foundations on free vibration behavior of FG beams [10,19,31,47].”